AC Magnitude and Phase
Objectives:
Today's experiment provides practical experience with the meaning of magnitude and phase in a linear
circuits and the use of phasor algebra to predict the response of a linear system to a sinusoidal input.
Using the digital oscilloscopes, we can better understand the true implications of amplitude and phase.
Pre Lab:
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Read and understand Hambley Sections 5.1 through 5.4
For v(t) = 160 Cos (180πt+ 60) determine:
1. Vmax
2. The phase angle θ.
3. The angular frequency ω.
4. Vrms
5. The phasor voltage V
Part A: RC Circuit Measurements
Procedure:
1. Set the output impedance of the function generator to Hi-Z mode.
2. Using any method, set the waveform generator for 500mV pk-pk using a 250 Hz sine wave.
3. Measure the 1k resistor using the Fluke 45 as an Ohmmeter. Measure the 1F capacitor using the
universal bridge on the instructor’s table. Enter these values on the data sheet.
4. Construct the RC circuit illustrated in Figure 1. Use the BNC to “micrograbber” cables to make
component connections,(remember to check that the amplification factor for CH1 and CH2 are
1x). When using the probes, use common sense precautions to avoid damaging the sensitive
contacts and clips.
Figure 1. The first positive peak for v1 occurs before the first positive peak of v2 so v1 leads v2. The
difference in time determines the phase difference between v1 and v2:   
t1  t 2
x360 . You can
T
also look at the time difference between zero crossings if it’s hard to tell exactly where the peaks of
the sine waves occur.
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NOTE: If the displayed wave is
extremely jumpy, the problem is
generally faulty leads or an
ungrounded probe. If you cannot
remedy the problem, ask for
assistance.
Figure 2: The RC Circuit
5. The display itself has a natural coarseness, which can be reduced by selecting the Average
function. Try to use as few samples as possible to avoid long delays while moving from one
display to another. Set both channels to the same Volts/Division setting. Averaging is a way to
pull a repetitive signal out of the background noise. It works better than a bandwidth limit or
brightness control because the bandwidth is not reduced. The simplest averaging is smoothing
(number of averages = 1). The oscilloscope acquires the signal every 5 ns. The smoothing
function uses two acquisitions to display one signal. The Average function (number of averages
>1) requires a stable trigger. The trigger is what tells the scope when to display the signal. It is
constantly acquiring the signal, but doesn’t let you see it until the signal meets some criteria you
set using the trigger controls.
6. Which channel appears to display the greater peak magnitude? Use the measure function to
determine the Voltage pk-pk amplitudes for both channels, and record in the data sheet.
7. AC Phasor analysis can determine the Complex Gain as a function of radian frequency.
Use measured values of your resistor and capacitor components to determine theoretical gain.
Measure the frequency in Hz using your oscilloscope and calculate the radian frequency. Record
the frequency, radian frequency, and theoretical gain value on your data sheet. Show all
calculations in your lab report.
Gain 
V2
1 / jC
1


V1 R  1 / jC 1  jRC
8. Calculate the ratio of the CH1 and CH2 pk-pk measurements to determine the measured gain and
record on your data sheet.
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9. We can also measure the phase. Position the time cursors on corresponding zero crossings (or peaks)
of the CH-1 and CH-2 waveforms. Determine the time difference t between the waves. Indicate
which channel arrives at the reference point first--this channel is said to "lead". Record these values
on the data sheet.
10. The measure function displays the wave periods. Record the period on the data sheet.
11. The phase shift, θ, is related to the time shift, Δt, that you observe on the oscilloscope . T is the
period of the waveform.

t
 360  t  f  360
T
Record the measured phase value on the data sheet.
12. We interpret the negative sign in the theoretical phase expression as revealing that the output "lags
behind" the input. That is, the input should lead the output. Describe in your lab report if this is what
you observed? What would be implied by an output that leads the input?
Part B: RL Circuit Measurements
1. Using any method, set the waveform generator for 200mV pk-pk using a 50 kHz sine wave.
2. Measure the 470 resistor using the Fluke 45 as an Ohmmeter. Measure the inductor using the
universal bridge on the instructor’s table. Make sure the bridge is set to Auto and 1 kHz when you
take your measurement. Enter this value on the data sheet.
3. Construct the RL circuit illustrated in Figure 2. Use the BNC to “micrograbber” cables to make
component connections,(remember to check that the amplification factor for CH1 and CH2 are
1x). When using the probes, use common sense precautions to avoid damaging the sensitive
contacts and clips.
4.
Which channel appears to display the greater peak magnitude? Use the measure function to
determine the Voltage pk-pk amplitudes for both channels, and record in the data sheet.
5.
Use AC phasor analysis to determine the voltage gain, which is the ratio of the output impedance
divided by the total series impedance. Show all calculations in your lab report.
Gain 
V2
V1
jL
) . Dividing through both sides by V1 yields the
R  jL
V
j L
complex gain for the circuit: Gain  2 
. This gain is sometimes called the “transfer
V1 R  jL
Using the voltage divider rule, V2  V1 (
function” since if we know the input voltage Phasor V1, we can determine the output voltage magnitude and
phase at any frequency. Try changing the frequency of the function generator signal, V1. What happens to the
amplitude of the output waveform V2 when you decrease the frequency? When you increase it?
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Figure 2: The RL Circuit
6. Use your measured component values to calculate the theoretical complex gain. Record these
theoretical magnitude and phase on the data sheet. Show all calculations in your lab report.
7. Calculate the ratio of the CH1 and CH2 pk-pk measurements to determine the measured gain
magnitude and record on your data sheet.
8. Measure the phase. Position the time cursors on corresponding zero crossings (or peaks) of the CH-1
and CH-2 waveforms. Determine the time difference t between the waves. Indicate which channel
arrives at the reference point first--this channel is said to "lead". Record values on the data sheet.
9. The measure function displays the wave periods. Record the period on the data sheet.
10. The phase shift, θ, is related to the time shift, Δt = t1 – t2, that you observe on the oscilloscope . T is
the period of the waveform.
 
t
 360  t  f  360
T
Record the measured phase value on the data sheet.
11. We interpret the negative sign in the theoretical phase expression as revealing that the output "lags
behind" the input. That is, the input should lead the output. Describe in your lab report if this is what
you observed? What would be implied by an output that leads the input?
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Data Sheet
Part A: RC Circuit Measurements
Nominal 1k resistor value____________
Nominal 1F capacitor value____________
Which channel has the great peak magnitude?
CH-1
CH-1 ___________________
CH-2 ____________________
f ______________
 ______________
Theoretical Gain ____________________
Measured Gain ____________________
CH-2
(Circle One)
Theoretical Phase ____________________

t ______________________
Which channel leads? __________
T________________________
Measured Phase ____________________
Part B: RL Circuit Measurements
Nominal 470 resistor value____________
Nominal 1 mH inductor value__________
Which channel has the great peak magnitude?
CH-1
CH-1 ___________________
CH-2 ____________________
f __________
 ______________
Theoretical Gain ____________________
Measured Gain ____________________
CH-2
(Circle One)
Theoretical Phase ____________________
t ______________________
Which channel leads? __________
T________________________
Measured Phase ____________________
Your Name_____________________________
Lab Instructor___________________
Partner Name___________________________
Date___________________________
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